2003-08-04
1984 VP-1001 CPU, 250 MFLOPS, 128 MB 2004ASCI Purple (LLNL)64 CPU 197, 100 TFLOPS, 50 TB, 4.5 MW PC 2 CPU 16, 4 GFLOPS, 32 GB, 3.2 kw 20028 CPU 640, 40 TFLOPS, 10 TB, 10 MW (ASCI: Accelerated Strategic Computing Initiative! Advanced Simulation and Computing Program)
analysis synthesis 1. 2. 3. 4. 5. 6. 7.
イオン 電子 クーロン力
dr j dr j = v j ; dv j = q m = v jke k + v drift (R j ;μ j ; t); dv jk (1) r j v j h i E(r j ; t) + v j B(r j ; t) dt dt R=μ= = q m E k(r j ;μ j ; t) dt dt
@n s @ρ m + @ @r (n su s ) = 0; n s m s du s = @p s fl m ρ p (2) (r; v) f (r; v; t), f (R;μ;v k ; t) (r) n(r; t), u(r; t), p(r; t) ψ! @ f f @ + v @ f @t @ f v B(r; t)] [E(r; = + t) @v coll @t @r + q m ψ! f Λ @ k e k + v drift (R;μ;t) @ f v + q m E k(r;μ;t) @ f = @v + k @r @t @ f coll @t d pn fl = 0 dt @t @r + n sq s (E + u B) + R s ; dt @ (ρ du mu) = 0; ρ m + = @p dt @r + j B; E + u B = j; d = 0 @t @r dt
(3)
r 2 Φ = ρ ext = 0 r 2 A k = μ 0 j k ; r 2 Φ = ρ ext = 0 ) 2 1=d r E = @B ; @t B = 1 c 2 @E @t + μ 0 j r
1. (consistency) 0 2. (accuarcy) 3. (stability) 4. (eciency)
(1) Lipschitz
(2) Explicit x (n+1) = F(x (n) ; t) t L x V V < x= t Implicit x (n+1) = F(x (n) ; x (n+1) ; t)
(3) (!$ I $ A) x = 0 $ A(!) x = 0 $ A(!) x = jxj!
CPU CPU CPU CPU CPU CPU Memory CPU CPU CPU CPU CPU CPU CPU Mem Mem Mem Mem Mem Mem CPU
=) 32bit CPU CPU 12 GB 64bit CPU : CPU 2 GB
ο 0:1mm ο 0:1mm ο 3mm ο 30 mm ο 1m ο 3m 140 GHz ο 100 GHz ο 100 GHz ο 3GHz ο 50 MHz ο 100 khz ο 10 khz ο 1s ο 1s ο EC LH IC MHD
(1) JFT-2M OFMC
(2)
70 20 TASK/WR Poloidal angle Toroidal angle beam 2m curvature Initial Ray/Beam Pro le Initial beam radius 0:05 m P abs Pro le j CD Pro le
f = 200 GHz, N = 0:2, r = 0:05 m r = 1:5m r=0.05 m r=1.5 f(p 0,p 0 )-f (-p 0,p 0 ) = f(p 0,p 0 ) = f = 200 GHz, N = 0:2, r = 0:05 m TASK/FP
=)
E θi P e E θi ITER P e ρ ρ TASK/WM
(3) DIII-D, JT-60 ITER JT-60 ITER JET, DIII-D
(1) Ware
@B 3 = @ @ρ = 1 V 0 @ + S s V 0 hjrρji 3 2 n st s V Es V 0 hjrρj 2 in s χ s @T s 0 B V *jrρj 2 R 2 + FR 0 hr 2 i hj Bi ext + P s (2) V:ρV 0 = dv=dρ 1 @ 0 V @t (n sv 0 ) = @ hjrρjin s V s hjrρj 2 id s @n s @ρ @ρ 1 @ 05=3 V 2 n st s V 05=3 @ρ @ρ @t» 0 F R 2 @ V 0 0 μ @ρ @t FR 0 hr 2 i F
χ TB = F(s;ff;»;! E1 ) ff 3=2! 2 pe >< >: 1 + G 1! 2 E1 1 + G 1! 2 E1 1 0 p 2s )(1 2s0 + 3s 02 ) 2(1 CDBM 2.5 F(s;ff;»;! E1 ) s ff c2 v A 2.0 ω E1 =0 ω E1 =0.1 1.5 dq F 1.0 ω E1 =0.2 ω E1 =0.3 qr s r q ff q 2 R dfi 0.5 dr» r R ψ dr 1 1 q 2! 0.0-0.5 0.0 0.5 1.0 s - α 8 qr de B A sv E B! E1 1 dr for s 0 = s ff < 0 F BM = 1 + p 2s 05=2 1 9 p 0 2s + 3s02 + 2s 03 ) 2(1 for s 0 = s ff > 0 E B
JT-60U : T [kev] Wdia [MJ] Ip [MA] τε / τε ITER89-P ne [10 19 m -3 ] TASK/TR Ip JT-60U T i (0.34a) t [s] Wdia t [s] n (0) t [s] t [s] T e (0) τ Ε / τ Ε ITER89-P P NBI Sn n (0.7) β N β N PNBI [MW] Sn [10 16 s -1 ] Ip [MA] Wdia [MJ] ne [10 19 m -3 ] T [kev] τ P NBI I BS n e (0) T i τ 1 W B t [s] t [s] t [s] <T e > t [s] Ip <n e > τ2 I OH <T i > Wi We T e τ Ε PNBI [MW] q T [kev] JT-60U r / a JT-60U r / a q t = 2.0 t = 2.8 t = 3.6 t = 4.4 t = 5.2 r [m] T [kev] t = 2.6 t = 2.5 t = 2.4 t = 2.3 t = 2.2 t = 2.1 t = 2.0 t = 2.8 t = 2.7 r [m] t [s] t [s]
@n s m s n s u s = 1 r @r (rn su sr ) + S s @r (rm sn s u 2 sr ) + 1 r m sn s u 2 s + e sn s (E r + u s B u s B ) @ @r n st s +F C s + FW s + FX s + FL s ψ 5 +P C s + PL s + PH s rn s m s μ s @r u s u s @ @t = 1 r @ @ @t (m sn s u sr )= 1 r ψ! @ sn s u s )= 1 @ r 2 (m @t @r (r2 m s n s u sr u s ) + e s n s (E u sr B ) + 1 r 2 @ r 3 n s m s μ s @ @r @r r NC s + F C s + FW s + FX s + FL s +F ψ! @ @ @ @ @t (rm sn s u sr u s ) + e s n s (E + u sr B ) + 1 r @r @r! @ r @r 2 u srn s T s n s χ s @ @r T e @ 3 + e s n s (E u s + E u s ) @t 2 n st s = 1 r
TASK/TX0:3m 2 =s10 m 2 =s JFT-2M NBI! =) =)
JFT-2M JFT-2M Ida et al.: Phys. Rev. Lett. 68 (1992) 182
ref: Z. Lin et al.: IAEA-2000 TH2-3
ref: W. Park et al.: IAEA-2002 TH5-1 (NTM) (RWM) (AE)
SOL JT-60U
EC LH IC MHD MHD MHD
ITER
TASK WR EQ WM TR DP FP
TASK EQ, TR, WR, WM EQ CDBM TR WR WM